DISORDER LINES AND NONMONOTONOUS RENORMALIZATION-GROUP FLOWS - APPLICATION TO THE 2-DIMENSIONAL XY-MODEL

We show analytically how the crossing of a disorder line in a simple onedimensional model coincides with a qualitative change of behaviour (monotonous to nonmonotonous) in the renormalization group flow. Such a change is found in Migdal-Kadanoff recursion relations of a family of ferromagnetic two-dimensional XY models. We therefore infer the existence of a disorder line in these models. For the usual XY model, the disorder temperature corresponds to the onset of short-distance pairing of vortices. It may coincide with the dynamical transition temperature recently found by Golinelli and Derrida. © 1990 The Japan Society of Applied Physics.